综合评价方法中的最优无量纲化模型研究  

Research on Optimal Dimensionless Models in Comprehensive Evaluation Methods

作　　者：李兴奇[1] 高晓红[2] Li Xingqi;Gao Xiaohong(School of Management and Economics,Chuxiong Normal University,Chuxiong Yunnan 675000,China;School of Mathematics and Computer Science,Chuxiong Normal University,Chuxiong Yunnan 675000,China)

机构地区：[1]楚雄师范学院管理与经济学院,云南楚雄675000 [2]楚雄师范学院数学与计算机科学学院,云南楚雄675000

出　　处：《统计与决策》2024年第5期44-49,共6页Statistics & Decision

基　　金：国家自然科学基金资助项目(11261001);云南省地方本科高校基础研究联合专项面上项目(202301BA070001-059;202301BA070001-054)。

摘　　要：针对综合评价过程中无量纲化方法选择盲目性较强的问题,文章首先引入综合评价结果优良性的度量指标,优化综合评价结果稳定性和区分度的度量函数,建立无量纲化有效性的统计检验方法;其次,以无量纲化有效为主要约束条件,分别以稳定性最高、区分度最高以及稳定性和区分度均最高为目标函数构建三类最优无量纲化模型,分析大平移尺度和小平移尺度约束条件对最优无量纲化模型的影响;最后,通过大量的数值模拟实验研究了6种常用综合评价方法中的最优无量纲化模型,并对结果进行深入分析。研究发现,大平移尺度约束下几种综合评价方法中的最优无量纲化结果均不同于现有无量纲化方法,小平移尺度约束下的最优无量纲化与均值化较为接近,但不完全相同;经过不断优化后的稳定性函数和区分度函数能更科学地度量综合评价结果的稳定性和区分度大小,无量纲化有效性的统计检验方法能准确判断指标间的量纲差异是否被有效消除;综合评价方法、目标函数和约束条件不同时所对应的最优无量纲化结果不同。Aiming at the blind selection of dimensionless methods in the process of comprehensive evaluation,this paper first introduces the measurement indicators of superiority of comprehensive evaluation results,optimizes the measurement functions of stability and differentiation degree of comprehensive evaluation results,and constructs a statistical test method for the effective-ness of the dimensionless methods.Secondly,taking the dimensionless effectiveness as the main constraint condition,the paper constructs three kinds of optimal dimensionless models with the objective functions of the highest stability,the highest differentia-tion degree and the highest stability and differentiation degree,analyzing the influences of large translation scale and small trans-lation scale constraints on the optimal dimensionless models.Finally,the paper carries out a large number of numerical simulation experiments to study the optimal dimensionless models in the six commonly used comprehensive evaluation methods,with the re-sults deeply analyzed.The results go as the following:Under the constraints of large translation scale,the optimal dimensionless results of several comprehensive evaluation methods are different from the existing dimensionless methods,and under the con-straints of small translation scale,the optimal dimensionless results are close to the mean value,but not identical.The stability function and differentiation degree function after continuous optimization can be used to measure the stability and differentiation degree of comprehensive evaluation results more scientifically,and the statistical test method of dimensionless effectiveness can be used to accurately judge whether the dimensional differences between indicators are effectively eliminated.Different compre-hensive evaluation methods,objective functions and constraint conditions lead to different optimal dimensionless results.

关 键 词：综合评价方法 最优无量纲化模型 稳定性 区分度 有效性 

分 类 号：O213.9[理学—概率论与数理统计]